Yea, as soon as I learned about cheesemaking, I realized these weren't 'presses'. Moulds maybe. I'm still puzzled about the circular indentations. And some of the moulds don't have very many draining holes.
I think these were first called cheese presses by the Victorians. Sometimes they got things right, sometimes not. The name has stuck. No-one I know has really studied these... yet. Cool, something to do in my copious spare time!
Thanks for all the replies. It's given me much to think about. Does anyone know of any other ceramic type moulds? I would think they would get awfully cold awfully quickly, unless used in a very warm environment. I really think I'll have my friend the potter make one of these moulds, just to see.